Kobuchi, Takashi

Mimura, Mikio

Mita, Masatoshi

Sato, Kuninori

Tsuji, Hiroshi

Osaka City University Repository

Mem. Fac. Eng., Osaka City Dniv., Vol. 39, pp. 77 -87 (1998)
Spatial Distribution of He I 5876A & He n 4686A Line Radiation
of TPD-S Plasma and Its Computer Simulation
Hiroshi Tsuji* , Masatoshi Mita* ,Mikio Mimura* ,
Takashi Kobuchi** and Kuninori Sato**
(Received September 30, 1998)
Synopsis
The plasma created by the T~D-S machine of National Institute for Fusion Science changes its shape
depending on the discharge current and the density in the experimental region. We measured the spatial
distribution ofthe intensity ofHe atomic line (5876A) and ionic line (4686A) emitted by the plasma. In order
to explain the distribution, we carried out a numerical simulation by integrating the rate equ~tions. A suitable
electron temperature distribution may explain the measured spatial distribution ofthe line intensity.
Keywords : stationary plasma, TPD-S machine, rate equation, digital camera
Introduction
The TPD-S (Test Plasma by Direct current discharge for Spectroscopy) machine of National Institute for
Fusion Science was built for the fundamental study of plasma spectroscopy. It creates a plasma with high
degree of ionization and small noise.
The shape of the plasma created by this machine considerably changes when the discharge current and the
introduced gas density are varied. For example, it is a simple cylindrical plasma whose emission strongly
extends along the center axis or double structure of a cylindrical plasma and halo around it. In some condition,
the emission spatially disappears and then appears once again. We took monochromatic image of helium line
spectrum of these plasmas by a digital camera and interference filters. The spatial distribution of the intensity
of these line spectrums is obtained from the image data. To explain the spatial distributions, we made a
computer simulation on the helium line intensity using rate equations. When we assumed a suitable electron
temperature distribution for each plasma discharge current, the calculated spatial distribution of the light
intensity resembles to that ofthe experiment data.
*Department ofApplied Physics, Faculty ofEngineering
** National Institute for Fusion Science (NIFS)
77
78
Experimental Setup and Result
The experimental setup is shown schematically in Fig I. The discharge is made between a cathode and an anode
which has a hole in the center. The floating electrodes are placed between the cathode and the anode to stabilize
the pressure gradient and to smooth the electric potential. The magnetic field is applies to confine the plasma on
center axis and to introduce the plasma to the anode hole. Helium gas is introduced from the back of the
cathode. The discharge voltage is 150V~160V and the discharge current is IOA"-'40A. The plasma flows
through the anode hole to the experimental region by the pressure gradient.
Three examples of plasma shape are shown in Fig. 2. They are taken from the window by the digital
6
I
Pump
Fig. 2 The schematic drawing ofTPD-S machine.
Mode A
Fig. 1 The shape ofmode A,B,C plasma.
79
camera (FUJIX DS-505) as a usual picture without the interference filter. Mode A plasma in Fig.2 is created
by 150V-35A discharge. The gas pressure in the discharge region and the experiment region is 5 Torr and
5 x 10-4 Torr respectively. A cylindrical plasma with a diameter ofabout 8mmeJ» which equals to that ofanode
hole flows out through the anode hole. Its emission extends along the center axis. Mode B plasma is created by
155V-25A discharge. The gas pressure in the discharge region and the experiment region is 10 Torr and
1 x 10-3 Torr respectively. There is a core plasma whose diameter is equal to that of anode hole. Enveloping
the core plasma, there is also a halo plasma whose diameter is approximately 80mmcJ». It is seen that both
plasma emissions disappear spatially on the way. Mode C plasma is created by 160V-10A discharge. The gas
pressure in the discharge region and the experiment region is 20 Torr and 5 X 10.3 Torr respectively. Similar to
the mode B plasma, a core plasma and a halo plasma are seen. Both the core and the halo plasma spatially
disappear, but appear once again.
Next, we took monochromatic images of the plasma using the digital camera with interference filters
(TOSmBA KL59 and KL46). From these images we got the spatial distributions ofthe intensity ofthe atomic
line (5876A) and the ionic line (4686A). Although the resolving power of the interference filter is low
(All2=140A), the filter is applicable because other line spectrum doesn't appear near 5876A and 4686A line.
The image consists of 1280 X 1000 pixels. It is stored in an uncompressed TIFF format file (24bit color mode).
To analyze the image, we have used NEOSLASHprogram(l) developed at our group. The program is written in
Quick Basic ofNEC PC 9801 computer. Using this program, it is possible to display x- or y-cross section,
bird's-eye view, histogram and so on.
.------------------.
Mode A
5876
Mode B
Mode C
Fig.3 The intensity distribution of 5876A line and 4686A line
along the center axis for A,B,C plasma.
80
At first we analyze the intensity distribution along the center axis. We omit the data near the anode hole
because of the saturation of ceD and the reflection of light by the wall. We performed Abel inversion of the
two dimensional monochromatic plasma image of HeI 5876A and HeB 4686A. Thus obtained intensity
distributions along the center axis are shown in Fig.3. In mode A plasma the intensity of both 5876A and
4686A lines extends along the center axis and decrease monotonously. We could not get the right half of the
5876Aline intensity because of an experimental mistake. In mode B plasma, the intensity of both lines
decreases rapidly and disappears. In mode C plasma, 5876A line disappears once and then appears again. As
for the 4686A line, only one peak is seen in this range. But there is bigger peak near the anode, where we omit
because of saturation. Therefore the 4686A line also disappears once and then appears again in the similar
way to 5876A line.
Computer Simulation using the Time History Method
To explain the intensity distributions ofthese line-spectra, we calculate them using the time history method by
rate equations. Time history method is originally applied to transient plasmas like Pinch or Tokamak(2)(3). To
apply this method to a stationary plasma, we used the relation between time and position of plasma in a
following way. As shown in Fig.4, the plasma flows out ofthe anode hole and moves as a function oftime. The
Anode y'i~~-~(!2~j.!~!_Q~~~!~-l
I
,._~fi$ilt~~~~1?Jf~~~:~~~~~~~ft:~~~;~··
I
I
________________________ J
I •Anode Hole
t:O
Fig.4 The image view ofthe conversion the location ofthe plasma to the time.
plasma traverses the field ofview ofthe digital camera (30 em) in about 0.3 ms due to the thermal velocity. We
solve the rate equations in the time interval between t =0 ms and 0.3 ms, where t =0 ms corresponds to the
position ofanode hole. The rate equations to be solved are;
dnt n t
-- = -Stnent + rtn en 2 --dt f'
dn2 n2
-- = Stnent - rtnen 2 - s2n en2+ r2n en2--~ f'
dn3 n3
-- = s2nen2 - r2nen3--dt f'
81
where n1 , n2 and n3 mean the density of He, He + and He 2+ respectively, SI and S2 are the ionization rate
coefficient from He to He+ and from He+ to He 2+respectively, 'I and r2 are the recombination rate
coefficient from He+ to He and He 2+ to He+ respectively. To include the density decrease due to plasma
expansion, we introduce an attenuation coefficient t.
Grotorian diagram of He and He+ is shown in Fig.5. Only the excitation from the ground state and
'n;=;oo
n=:2.
15 ~'p ·:tn··.. .
12---
!
~
r
i
I
:~.
He
n=CO :.....--...-.Ill
n=4
n=2
Be~
Fig.5 The Grotorian diagram of He and He+ in the range from the quntum number of
n= I to n=4. The 5876A line is emitted by the transition from 33 D to 2 3 P and
the 4686A line is from n =4 to n =3.
recombination from the continuous level are taken into account. The intensity of5876A line and 4686A line
is written as;
I(5876A) =ne (OV)1 n1 + neGR1(3)n2
A
I(4686A) =(n
e
(OV)2 n2 + neR2 (4)n3 ) x 43A41 + A42 + A43
where (01')) and (OV)2 mean the excitation rate coefficient of He and He+ respectively, R1(3) is the
recombination rate coefficient from the continuous level of He+ to the n =3 state of He, R2 (4) is that from
the continuous state of He 2+ to the n =4 state of He+, G is the ratio of the statistic weight of 33 D state to
the sum ofthat of all the n =3 levels (Le. G =7 / (1 + 3 + 5 + 3 + 5 + 7) =0.292 ) and Aij is the transition
probability between i state and j state.
Therefore, the emission intensity depends on the eleven parameters; the electron density ne , the atom and ion
density nl , n2 ,n3 , the excitation rate coefficients (ov) 1 ,(OV)2' the recombination rate coefficients 71,72 , the
ionization rate coefficients SI' S2 and the attenuation coefficient t. But as shown below, it actually depends on
the three independent parameters; electron temperature Te, the sum of the atom and ion density
N (=nl + n2 + n3 ) and the attenuation coefficient t.
i) The Electron Density .
Because the plasma is electrically neutral, the electron density is derived from the ion density;
ne =n2 + 2· n3
82
ii) The Ionization, Excitation and Recombination rate Coefficients
The ionization rate coefficient is given as the following relation(4);
Sj = e-I';Te(~~);{to an(IOglo(~~))n em 3 /s,
where Te is the electron temperature, Ii is the ionization potential and an is a coefficient which depends on
the atom species. Figure 6 shows the dependence on the electron temperature.
"iii"1 -8
100
Temperature reV]
Fig. 6 The ionization rate coefficient.
The excitation rate coefficient is given as the following relation(5);
(ov)z = 1.70 x 10-3(Te.1l600r~Eijlfjj · p(y). exp(-y) em3Is
p(y) =A +(By-Cy2 +D).(ln(Y+l) - 0.4 2) +~y
Y (y+l) ,
where E ij is the excitation energy, f ij is the oscillator strength, A, B, C and D are the coefficients ofMewe,
and y = Ii / Te. Z is unity or two. Figure 7 shows the dependence on the electron temperature.
Temperature [eV]
Fig. 7 The excitation rate coefficient
83
The recombination rate coefficient from He + to He and from He 2+ to He + are given;
00 00
7] = 2· R] (1) + LR; (i) and 72 = LR2 (i) (6),
i=2 i=]
where
R (i) =2.607 x 10-12 _Z_4 •(Ter% ·(IOg-Y_+_l - _0._4_J
Z j3 y (y + 1)2
Figure 8 shows the dependence on the electron temperature.
Fig. 8 The recombination rate coefficient
iii) The Attenuation Coefficient
The plasma density near the center axis decreases because the plasma flows with expansion. To include
this effect in the equations, we introduced the attenuation coefficient.
iv) The Initial Values ofthe Density ofAtom and Ions
The initial values of n] ,n2 and n3 can't measured. We assume that the plasma in the discharge region is
stationary; dn; / dt = o. Then from the rate equations and N = n] +n2 +n3 , we get following relations;
n] =r] · r2 / s] · N/(r] · r2 / s] + S2 + 72 )
n2 = r2 • N / (r1 • r2 / S1 + S2 + 72 )
n3 = S2 • N / (r] · r2 / S] + S2 + r2 )
therefore if the initial values of N and electron temperature are given, the initial values of n1 ,n2 and n3 are
obtained.
Now the intensity distribution of the emission can be calculated if the electron temperature distribution, the
attenuation coefficient, and the sum of the atom and the ion density are given. The data necessary for the
calculation are summarized in Table 1. We calculated the line intensity distribution by changing these three
parameters. A good agreement with the experimental result was obtained when f' =0.04 ms. We fixed this
parameter and changed the initial value of N and the electron temperature distribution so that the calculated
intensity distribution agrees to the measured intensity distribution.
84
(a) Data necessCln' for the calculation ofthe ionization rate coefficients
I.P.feV] ao a1 a2 a3 a4 as
He 24.587 1.500E-8 5.666E-I0 -6.082E-9 -3.589E-9 1.553E-9 1.320E-9
He+ 54.416 3.436E-9 -1.687E-9 -6.924E-I0 9.786E-ll 1.559E-I0 6.224E-ll
(b) Date necessary for the calculation ofthe recombination rate coefficients
• He+ --+ He
Level I.P.[eV] Statistic Level I.P.[eV] Statistic Level I.P.[eV] Statistic
Weight Weight Weigh
lIS 24.59 1 31D 1.51 5 4 1D 0.85 5
2 1S 1.97 1 33 S 1.83 3 4 1F 0.85 7
2 1 p 3.37 3 33 P 1.54 5 4 3 S 0.96 3
2 3 S 4.73 3 33 D 1.48 7 4 3 P 0.84 5
2 3 S 3.59 5 4 1S 0.91 1 4 3 D 0.82 7
31S 1.67 1 4 1 p 0.84 3 4 3 F 0.82 9
31 p 1.50 3
Level I.P.[eV] Transition Probability[108s·11(8) Level I.P.[eVl
n=4 3.402 1.438(A43 } n=3 6.047
1.347(A42 } n=2 13.606
2.045(A41 } n=1 54.402
(c) Date necessary for the calculation of the excitation rate coefficients
Excitation Transition Excitation Oscillator Mewe's Coefficients(4)
Energy[eV] Strength
He(1 1S --+ 33D) 23.105 0.0734 A=B=D=O,C=O.1
He+ (n =1--+ n =4) 51.020 0.0290 A=0.25,B=0.04,C=0,D=0.28
Table 1 Data necessary for calculating the ionization, recombination and excitation
rate coefficients.
The result of the calculation for the mode A plasma is shown in Fig.9. The top shows the electron
temperature, which is varied from 5.5 eV to 5 eV in 0.3 ms. The center shows the density. It is seen that the
He+ ion is dominant in this temperature region. Because of the attenuation coefficient, all of the He ,He+ and
He 2+ density decrease gradually. The excitation rate coefficient also decreases due to the temperature drop. So
the intensity ofboth ofthe atomic 5876A line and ionic 4686A line also decrease.
85
Mode A
Electron Temperature
Line Intensity
5876A
4686A
O.3[ms]
Fig.9 The simulation result ofthe mode A plasma
The result of the calculation for mode B plasma is shown in Fig. IO. This time, the temperature drops
exponentially from 5.5 eV to 1.0 eV in 0.3 ms. Similar to the mode A case, the He+ and He 2+ density
decrease. However, recombination takes place as a result of the sharp temperature drop and the He density
increases. Because of this density increase, the decrease of 5876A line intensity is small near the anode hole.
Although the recombination takes place, the main process for the emission of the 5876A line in this
temperature region is excitation. Thereafter, the 5876A line decreases and disappears before 0.3 ms due to
low temperature. As for the 4686A line, because both ofthe decrease of He+ density and the excitation rate
coefficient, its emission disappears as soon as the plasma flows out of the anode hole. The calculated result
differs from the measured result, in which the 4686A line disappears in similar way to the 5876A line as
shown in Fig.3.
ModeB
5. rat~re _
t91c5enf
3 Densit~~_e+ _
0 92+ He(X 10)
2e17cm~-1 : Line Intensity
Fig. 10 The simulation result of the mode B plasma
The result ofthe calculation for mode C is shown in Fig.ll. This time, the temperature drops exponentially
from 5.5 eV to 1.2 eV in 0.12 ms and thereafter drops from 1.2 eV to 0.1 eV in 0.03 ms. When the temperature
drops in such a rapid way, the He density increases sharply and the He 2+ density decreases also sharply.
Then recombination occurs more actively than the Mode B case. The intensity of both of the 5876A line and
86
the 4686A line which decreases when the plasma leaves the anode hole, shows a sudden increase. This is in
good agreement with the intensity distribution observed in the experiment. Therefore the reappearance of the
5876A line and the 4686A may be explained by the recombination due to the rapid electron temperature
drop.
ModeC
5. emperature
5ej J1e+
~------
1818
1
~~.1 j Line Intensity~Jl !5876.A
468r _ ~
I, ~----
o O.3[ms]
Fig. II The simulation result ofthe mode C plasma
Conclusion
Using a digital camera and interference filters, we measured the spatial intensity distribution of He I 5876A
line and He II 4686A line for three discharge modes of TPD-S plasma. By the inverse Abel transformation,
the axial intensity distribution of these two lines are obtained.
We performed a simulation oftheir intensity distribution using rate equations. When we assumed a suitable
electron temperature distribution, the initial value ofthe density ofatom and ion, and an attenuation coefficient,
the calculated intensity distribution of the two lines agreed quite well to the measured distribution. In this way
the reappearance ofthese two lines observed in the mode C plasma was explained by the recombination process
due to a rapid electron temperature drop.
The occurrence of such a rapid temperature drop may be explained by the three-body recombination
process. When the plasma is high density and low electron temperature like mode C plasma, the effect of
three-body collision and the kinetic energy loss of electrons may not be ignored. Such three-body recombination
effect, however, is not taken into consideration so far. The inclusion of this effect in the rate equations will be
the next research theme.
Acknowledgments
This work was carried out under a collaborating research program at the National Institute for Fusion Science.
87
References
1) T.Uneyama: Master Thesis (in Japanese), Faculty of Engineering Osaka City University, 1998.
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3) M.Mimura, D.D.Meyerhofer, S.F.Paul and P.Young: 7th Symp. on Compact Torus Symposium,
Santa-Fe (1985) 25.
4) K.L.Bell, H.B,Gibody, J.G.Hunghes, A.E.Kingston, and F.J.Smith: "Atomic and Molecular
Data for Fusion Part I" ,CLM-R216 December (1981).
5) M.Arnaud and R.Rothenflug : Astron.Astrophys.Suppl. 60 (1985) 425.
6) T.Kato: IPPJ-AM-2, June 1977.
1) M.J.Seaton: Mon.Not.R.Astron.Soc. 119 (1959) 81.
8) W.L.Wiese, M.W.Smith, and B.M.Glennon: National Standard Reference Data Series, National
Bureau of Standards 4 (1966).


Spatial Distribution of He I 5876A & He II 4686A Line Radiation of TPD-S Plasma and Its Computer Simulation

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Spatial Distribution of He I 5876A & He II 4686A Line Radiation of TPD-S Plasma and Its Computer Simulation

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